A lot, as the Low Salt Queen has recently learned! Aside from the obvious listing of the various nutritional values, the wording and structure of a product's label is governed in the United States by the Food and Drug Administration. The FDA has strict guidelines for the way products may be labeled, and sometimes what the label doesn't say can be as compelling as what it does say!
Here are the FDA Regulations for general product claims, and specific claims for sodium. You can click it to "embiggen":